The purpose of this model is to understand how genetic architectures of alternative reproductive tactics impact their maintenance in populations. I’m using an individual-based simulation model with different selection scenarios, types of alternative tactics, and genetic architectures (genome-wide additive genetic variance, supergenes, expression networks).

## Package 'sm', version 2.2-5.6: type help(sm) for summary information

Here, I’m presenting the initial sensitivity analysis results. I tested the effects of four parameter settings: mating system, the ratio of reproductive allocation between courters and non-courters, the survival of parental male nests, and the survival of non-parental male nests.

By ‘mating system’ I refer to whether males are able to mate with multiple females (i.e., be the nesting male for multiple females). The default is monogamy, meaning males can only be the nesting male to one female.

The ratio of reproductive allocation between courters and non-courters comes into play during the fertilization stage of the model. At this point, females have mated with a male, and her eggs will be preferentially fertilized by her mate but could also be fertilized by non-courting males. Each male has a maximum reproductive success or reproductive allocation that is given by their courtship status ($r_{courter}$ or $r_{non-courter}$) and gets used up by each additional fertilization. This sets a bound on reproductive success for each male. When a female mates, she receives a total of $\Sigma{n_{sperm}}$ from all of the males who attempt to fertilize her eggs (e.g., with one courter and two non-courters, $\Sigma{n_{sperm}}$ = $r_{courter}$ + 2$*$(0.5$*$$r_{non-courter}$)). The ratio of $r_{courter}$ to $r_{non-courter}$ is the parameter set that I varied in these sensitivity analyses.

The final two traits that I tested were the survival of a nest when it was with parental male and the survival of a nest when it was with a non-parental male. I tested these two parameters separately. When the parental nest survival parameter was tested the non-parental nest survival was constant at 0.1. When the non-parental nest survival parameter was tested the parental nest survival was constant at 0.9.

I tested several parameter settings with three genetic architectures and with just a courter trait, just a parent trait, and both traits:

The parameters, their defaults, and their tested settings
parameter	default	tested_settings
polygyny	monogamy	polygyny
relative reproductive allocation (courter:non-courter)	8:4 (2)	2:8 (0.25), 4:8 (0.5), 4:4 (1), 8:2 (4)
parental nest survival	0.9	0.5, 0.6, 0.7, 0.8
non-parental nest survival	0.1	0.2, 0.3, 0.4, 0.5

Here, I present the initial analyses of those parameter combinations.

Courter Trait

Summaries of final morph frequencies
param_label	params	CourterFreqMean Unlinked	CourterFreqMean Linked	CourterFreqMean Supergene
polygyny_1	FALSE	1	1	1
polygyny_1	TRUE	1	1	1
crs2_ncrs8_1	0.25	1	1	1
crs2_ncrs8_1	0.5	1	1	1
crs2_ncrs8_1	1	1	1	1
crs2_ncrs8_1	4	1	1	1
crs2_ncrs8_1	2	1	1	1
psurv0	0.5	1	1	1
psurv0	0.6	1	1	1
psurv0	0.7	1	1	1
psurv0	0.8	1	1	1
psurv0	0.9	1	1	1
npsurv0	0.1	1	1	1
npsurv0	0.2	1	1	1
npsurv0	0.3	1	1	1
npsurv0	0.4	1	1	1
npsurv0	0.5	1	1	1

When just the courter trait is present, regardless of the parameter settings, the courting male morph goes to fixation in every run.

Parent Trait

Summaries of final morph frequencies
param_label	params	ParentFreqMean Unlinked	ParentFreqMean Linked	ParentFreqMean Supergene
polygyny_1	FALSE	1	1	1
polygyny_1	TRUE	1	1	1
crs2_ncrs8_1	0.25	1	1	1
crs2_ncrs8_1	0.5	1	1	1
crs2_ncrs8_1	1	1	1	1
crs2_ncrs8_1	4	1	1	1
crs2_ncrs8_1	2	1	1	1
psurv0	0.5	1	1	1
psurv0	0.6	1	1	1
psurv0	0.7	1	1	1
psurv0	0.8	1	1	1
psurv0	0.9	1	1	1
npsurv0	0.1	1	1	1
npsurv0	0.2	1	1	1
npsurv0	0.3	1	1	1
npsurv0	0.4	1	1	1
npsurv0	0.5	1	1	1

When just the parent trait is present, regardless of the parameter settings, the parental male morph goes to fixation in every run.

Courter and Parent Traits

Summaries of final morph frequencies when QTLs are unanchored
param_label	params	FreqNcNpMean	FreqNcNpSEM	FreqNcPMean	FreqNcPSEM	FreqCNpMean	FreqCNpSEM	FreqCPMean	FreqCPSEM
polygyny_1	FALSE	0.0000000	0.0000000	0.0000000	0e+00	0.4000000	0.0251312	0.6000000	0.0251312
polygyny_1	TRUE	0.0000000	0.0000000	0.0000000	0e+00	0.6666667	0.0410305	0.3333333	0.0410305
crs2_ncrs8_1	0.25	0.0000000	0.0000000	0.0000000	0e+00	1.0000000	0.0000000	0.0000000	0.0000000
crs2_ncrs8_1	0.5	0.0084754	0.0013261	0.0000000	0e+00	0.3333333	0.0410305	0.6581912	0.0405272
crs2_ncrs8_1	1	0.0000000	0.0000000	0.0002546	9e-05	0.9997454	0.0000900	0.0000000	0.0000000
crs2_ncrs8_1	4	0.0000000	0.0000000	0.0000000	0e+00	0.5000000	0.0668153	0.5000000	0.0668153
crs2_ncrs8_1	2	0.0000000	0.0000000	0.0000000	0e+00	0.4000000	0.0251312	0.6000000	0.0251312
psurv0	0.5	0.0026771	0.0004584	0.0000000	0e+00	0.3333333	0.0410305	0.6639896	0.0408680
psurv0	0.6	0.0000000	0.0000000	0.0000000	0e+00	0.6666667	0.0410305	0.3333333	0.0410305
psurv0	0.7	0.0006808	0.0001528	0.0000000	0e+00	0.6666667	0.0410305	0.3326525	0.0409469
psurv0	0.8	0.0011888	0.0002446	0.0000000	0e+00	0.6666667	0.0410305	0.3321445	0.0408846
psurv0	0.9	0.0000000	0.0000000	0.0000000	0e+00	0.4000000	0.0251312	0.6000000	0.0251312
npsurv0	0.1	0.0000000	0.0000000	0.0000000	0e+00	0.4000000	0.0251312	0.6000000	0.0251312
npsurv0	0.2	0.0004865	0.0000734	0.0000000	0e+00	0.6666667	0.0410305	0.3328468	0.0409706
npsurv0	0.3	0.0008341	0.0000860	0.0000000	0e+00	0.0000000	0.0000000	0.9991659	0.0000860
npsurv0	0.4	0.0000000	0.0000000	0.0000000	0e+00	0.6666667	0.0410305	0.3333333	0.0410305
npsurv0	0.5	0.0017481	0.0003617	0.0000000	0e+00	0.3333333	0.0410305	0.6649186	0.0409244

Summaries of final morph frequencies when QTLs are anchored on chromosomes
param_label	params	FreqNcNpMean	FreqNcNpSEM	FreqNcPMean	FreqNcPSEM	FreqCNpMean	FreqCNpSEM	FreqCPMean	FreqCPSEM
polygyny_1	FALSE	0.0000000	0.0000000	0.0000000	0.0000000	0.1500000	0.0183174	0.8500000	0.0183174
polygyny_1	TRUE	0.0096222	0.0012585	0.0034947	0.0004354	0.0031582	0.0005009	0.9837249	0.0021082
crs2_ncrs8_1	0.25	0.0000000	0.0000000	0.0000000	0.0000000	0.8750000	0.0441942	0.1250000	0.0441942
crs2_ncrs8_1	0.5	0.0005088	0.0000768	0.0000000	0.0000000	0.0000000	0.0000000	0.9994912	0.0000768
crs2_ncrs8_1	1	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	1.0000000	0.0000000
crs2_ncrs8_1	4	0.0190862	0.0027853	0.0039816	0.0006871	0.0130262	0.0022630	0.9639060	0.0053446
crs2_ncrs8_1	2	0.0000000	0.0000000	0.0000000	0.0000000	0.1500000	0.0183174	0.8500000	0.0183174
psurv0	0.5	0.0090727	0.0013769	0.0030870	0.0004369	0.3344015	0.0408759	0.6534388	0.0402612
psurv0	0.6	0.0001740	0.0000502	0.0000000	0.0000000	0.6666667	0.0410305	0.3331593	0.0410091
psurv0	0.7	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	1.0000000	0.0000000
psurv0	0.8	0.0000000	0.0000000	0.0001736	0.0000501	0.2500000	0.0376889	0.7498264	0.0376802
psurv0	0.9	0.0000000	0.0000000	0.0000000	0.0000000	0.1500000	0.0183174	0.8500000	0.0183174
npsurv0	0.1	0.0000000	0.0000000	0.0000000	0.0000000	0.1500000	0.0183174	0.8500000	0.0183174
npsurv0	0.2	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	0.0000000	1.0000000	0.0000000
npsurv0	0.3	0.0000000	0.0000000	0.0000000	0.0000000	0.0833333	0.0240563	0.9166667	0.0240563
npsurv0	0.4	0.0003315	0.0000645	0.0000000	0.0000000	0.0000000	0.0000000	0.9996684	0.0000646
npsurv0	0.5	0.0000000	0.0000000	0.0000000	0.0000000	0.6666667	0.0410305	0.3333333	0.0410305

Summaries of final morph frequencies when QTLs are in a supergene
param_label	params	FreqNcNpMean	FreqNcNpSEM	FreqNcPMean	FreqNcPSEM	FreqCNpMean	FreqCNpSEM	FreqCPMean	FreqCPSEM
polygyny_1	FALSE	0.0000000	0.0000000	0.0000000	0.0000000	0.2000000	0.0205196	0.8000000	0.0205196
polygyny_1	TRUE	0.0000000	0.0000000	0.0391371	0.0075034	0.5441617	0.0403551	0.4167013	0.0390665
crs2_ncrs8_1	0.25	0.0000000	0.0000000	0.1115314	0.0150801	0.6383412	0.0483446	0.2501275	0.0334706
crs2_ncrs8_1	0.5	0.0022491	0.0003896	0.0000000	0.0000000	0.3333333	0.0410305	0.6644176	0.0408937
crs2_ncrs8_1	1	0.0000000	0.0000000	0.0010593	0.0003745	0.0000000	0.0000000	0.9989406	0.0003745
crs2_ncrs8_1	4	0.0007389	0.0001275	0.0000000	0.0000000	0.0000000	0.0000000	0.9992611	0.0001275
crs2_ncrs8_1	2	0.0000000	0.0000000	0.0000000	0.0000000	0.2000000	0.0205196	0.8000000	0.0205196
psurv0	0.5	0.0000000	0.0000000	0.0001725	0.0000498	0.9998275	0.0000498	0.0000000	0.0000000
psurv0	0.6	0.0000000	0.0000000	0.0000000	0.0000000	0.3333333	0.0410305	0.6666667	0.0410305
psurv0	0.7	0.0000000	0.0000000	0.0000000	0.0000000	0.3333333	0.0410305	0.6666667	0.0410305
psurv0	0.8	0.0000000	0.0000000	0.0011981	0.0002977	0.3335000	0.0410203	0.6653019	0.0409475
psurv0	0.9	0.0000000	0.0000000	0.0000000	0.0000000	0.2000000	0.0205196	0.8000000	0.0205196
npsurv0	0.1	0.0000000	0.0000000	0.0000000	0.0000000	0.2000000	0.0205196	0.8000000	0.0205196
npsurv0	0.2	0.0000000	0.0000000	0.0000000	0.0000000	0.0003366	0.0000656	0.9996634	0.0000656
npsurv0	0.3	0.0000000	0.0000000	0.0000000	0.0000000	0.6666667	0.0410305	0.3333333	0.0410305
npsurv0	0.4	0.0000000	0.0000000	0.0000000	0.0000000	0.6666667	0.0410305	0.3333333	0.0410305
npsurv0	0.5	0.0000000	0.0000000	0.0135000	0.0026410	0.5839322	0.0390511	0.4025678	0.0389282

The outcomes are not as consistent with both traits present, and it may be easier to visualize with plots.

Unlinked QTLs

We’ll start by looking at the unlinked QTLs.

Polygyny

Frequency of morphs with unlinked QTLs in scenarios with and without polygyny

Looking at these figures, the outcomes are consistent across mating systems: in all cases, either the Courter-Parent or the Courter-Nonparent morphs are fixed.

Reproductive Allocations

Frequency of morphs with unlinked QTLs in scenarios with different ratios of courter to non-courter reproductive success

For the ratio of reproductive allocations, the parameter settings do affect the outcomes. In the cases when the Courter has a higher allocation – both 8 to 4 (ratio = 2) and 8 to 2 (ratio = 4) – the outcomes are variable, with either the Courter-Parent or Courter-Nonparent morphs being fixed. When the non-courters have a much higher reproductive allocation than courters (8 offspring compared to 2, ratio = 0.25), the Courter-Parent morph is never fixed, and instead the Courter-Nonparent morph is fixed. This pattern is also found when Courters and Noncourters have equivalent allocations (4 and 4). Intriguingly, at the ratio of 0.5, when Noncourters have an allocation of 8 and Courters have an allocation of 4, variation is maintained in a handful of the simulations, with a very small number of Noncourter-Nonparent morphs still occurring in the population along with Courter-Parent morphs.

Parental nest survival

Frequency of morphs with unlinked QTLs in scenarios with different survival rates for nests of the parental morph

Parental nest survival does not appear to have a major effect on the outcomes. Occasionally, at several of the lower survival rates (0.5, 0.7, 0.8) a very small proportion of males have the Noncourter-Nonparent morph when the vast majority of males have the Courter-Parent morph.

Non-parental nest survival

Frequency of morphs with unlinked QTLs in scenarios with different survival rates for nests of the parental morph

No major effects observed, although when non-parent nest survival was 0.3 every run had the outcome of fixed Courter-Parent morph, whereas in other cases the Courter-Nonparent morph was also fixed occasionally. In the case where survival was 0.5, one or two runs maintained tiny amounts of polymorphism, with near-zero positive frequencies of Noncourter-Nonparent morphs occurring alongside the Courter-Parent morphs.

Linked QTLs

Allele frequencies in the final generation of all of the runs - baseline

Trait values in the final generation of all the runs: baseline with linked QTLs

Polygyny

Frequency of morphs with linked QTLs in scenarios with and without polygyny

With linked QTLs, the mating system has an effect. Polygyny allows variation to be maintained, with every run resulting in a population of mostly Courter-Parents, but some small numbers of Courter-Nonparents, Nonparent-Courters, and/or NonCourter-Nonparents. From the way these results are presented, it’s challenging to determine whether all three morphs are maintained in the same run. To get at that, we can plot each run’s outcomes:

Frequencies over time in each run with linked QTLs, both traits, and polygyny

It appears that in one set of runs, all three morphs are maintained simultaneously.

Allele frequencies in the final generation of all of the runs - polygyny

Interestingly, genetic variation is found in the runs that don’t have polymorphism either (but remember that allele frequencies are not necessarily reflective of additive genetic variation).

Trait values in the final generation of all the runs: polygyny with linked QTLs

Reproductive Allocations

Frequency of morphs with linked QTLs in scenarios with different ratios of courter to non-courter reproductive success

In general, high ratios generally result in Courter-Parent morph to be fixed, although at very high ratios some polymorphism with Noncourter-Nonparent is observed. At the lowest ratio, when Noncourters have 8 offspring and courters have 2, in almost all cases the Courter-Nonparent morph is fixed, with one exception where the Courter-Parent morph is fixed.

$Allele frequencies in the final generation of all of the runs - courter RS = 2, noncourter RS = 8$

Allele frequencies in the final generation of all of the runs - courter RS = 2, noncourter RS = 8

Trait values in the final generation of all the runs: courter RS = 2, noncourter RS = 8 with linked QTLs

Allele frequencies in the final generation of all of the runs - courter RS = 4, noncourter RS = 8

Trait values in the final generation of all the runs: courter RS = 4, noncourter RS = 8 with linked QTLs

Allele frequencies in the final generation of all of the runs - courter RS = 8, noncourter RS = 2

Trait values in the final generation of all the runs: courter RS = 8, noncourter RS = 2 with linked QTLs

Allele frequencies in the final generation of all of the runs - courter RS = 8, noncourter RS = 8

Trait values in the final generation of all the runs: courter RS = 8, noncourter RS = 8 with linked QTLs

Interestingly, genetic variation is maintained in all of them.

Parental nest survival

Frequency of morphs with linked QTLs in scenarios with different survival rates for nests of the parental morph

In general, the Courter-Parent or Courter-Nonparent traits become fixed, although with parental nest survival at 0.7 only the Courter-Parent morph became fixed (though this may be an artefact of not running huge numbers of runs).

Allele frequencies in the final generation of all of the runs - parent nest survival = 0.5

Trait values in the final generation of all the runs: parent nest survival = 0.5 with linked QTLs

Allele frequencies in the final generation of all of the runs - parent nest survival = 0.6

Trait values in the final generation of all the runs: parent nest survival = 0.6 with linked QTLs

Allele frequencies in the final generation of all of the runs - parent nest survival = 0.7

Trait values in the final generation of all the runs: parent nest survival = 0.7 with linked QTLs

Allele frequencies in the final generation of all of the runs - parent nest survival = 0.8

Trait values in the final generation of all the runs: parent nest survival = 0.8 with linked QTLs

Non-parental nest survival

Frequency of morphs with linked QTLs in scenarios with different survival rates for nests of the parental morph

In general, the Courter-Parent or Courter-Nonparent morph becomes fixed, although occasionally the Courter-Nonparent morph is fixed instead. The highest survival rate (0.5) allows the Courter-Nonparent morph to be fixed more frequently.

Allele frequencies in the final generation of all of the runs - non-parental nest survival = 0.2

Trait values in the final generation of all the runs: non-parent nest survival = 0.2 with linked QTLs

Allele frequencies in the final generation of all of the runs - non-parental nest survival = 0.3

Trait values in the final generation of all the runs: non-parent nest survival = 0.3 with linked QTLs

Allele frequencies in the final generation of all of the runs - non-parental nest survival = 0.4

Trait values in the final generation of all the runs: non-parent nest survival = 0.4 with linked QTLs

Allele frequencies in the final generation of all of the runs - non-parental nest survival = 0.5

Trait values in the final generation of all the runs: non-parent nest survival = 0.5 with linked QTLs

QTLs in a supergene

We’ll start by looking at the unlinked QTLs.

Allele frequencies in the final generation of all of the runs - baseline

Trait values in the final generation of all the runs: polygyny with a supergene

Polygyny

Frequency of morphs with a supergene in scenarios with and without polygyny

Similar to the case with linked QTLs, polygyny allows polymorphism to be maintained in some runs, this time with Courter-Parent, Courter-Nonparent, and Noncourter-Parent morphs all being maintained in the population.

Allele frequencies in the final generation of all of the runs - polygyny

When variation is maintained, the genetic variation maintained is much greater as well.

Trait values are recorded for each population at the final generation and written to the *traits.txt files.

Trait values in the final generation of all the runs: polygyny with a supergene

Reproductive Allocations

Frequency of morphs with a supergene in scenarios with different ratios of courter to non-courter reproductive success

Now polymorphism can be maintained when the ratios are very low. In one set of simulations when Noncourters had the reproductive advantage, the Courter-Parent morphs coexisted with Courter-Nonparents and Noncourter-Parents. Otherwise, similar patterns were observed with either Courter-Parent morphs of Courter-Nonparent morphs becoming fixed.

Genetic composition?

Let’s look at the final allele frequencies across all reps

Allele frequencies in the final generation of all of the runs - supergene and courter RS = 2, noncourter RS = 8

Trait values in the final generation of all the runs: courter RS = 2, noncourter RS = 8 with a supergene

Allele frequencies in the final generation of all of the runs - supergene and courter RS = 4, noncourter RS = 8

Trait values in the final generation of all the runs: courter RS = 4, noncourter RS = 8 with a supergene

Allele frequencies in the final generation of all of the runs - supergene and courter RS = 8, noncourter RS = 2

Trait values in the final generation of all the runs: courter RS = 8, noncourter RS = 2 with a supergene

Allele frequencies in the final generation of all of the runs - supergene and courter RS = 8, noncourter RS = 8

Trait values in the final generation of all the runs: courter RS = 8, noncourter RS = 8 with a supergene

Parental nest survival

Frequency of morphs with a supergene in scenarios with different survival rates for nests of the parental morph

Here, the lowest parental nest survival rate (0.5) resulted in all cases having the Courter-Nonparent morph becoming fixed, whereas in the other runs either the Courter-Parent or the Courter-Nonparent could become fixed.

Allele frequencies in the final generation of all of the runs - parent nest survival = 0.5

Trait values in the final generation of all the runs: parent nest survival = 0.5 with a supergene

Allele frequencies in the final generation of all of the runs - parent nest survival = 0.6

Trait values in the final generation of all the runs: parent nest survival = 0.6 with a supergene

Allele frequencies in the final generation of all of the runs - parent nest survival = 0.7

Trait values in the final generation of all the runs: parent nest survival = 0.7 with a supergene

Allele frequencies in the final generation of all of the runs - parent nest survival = 0.8

Trait values in the final generation of all the runs: parent nest survival = 0.8 with a supergene

Non-parental nest survival

Frequency of morphs with a supergene in scenarios with different survival rates for nests of the parental morph

High survival of the non-parental nests allows polymorphism to be maintained – Courter-Parent, Courter-Nonparent, and Noncourter-Parent morphs are all maintained at appreciable frequencies when survival was 0.5. In the other cases, either the Courter-Parent or the Courter-Nonparent morphs became fixed.

Allele frequencies in the final generation of all of the runs - non-parental nest survival = 0.2

Trait values in the final generation of all the runs: non-parent nest survival = 0.2 with a supergene

Allele frequencies in the final generation of all of the runs - non-parental nest survival = 0.3

Trait values in the final generation of all the runs: non-parent nest survival = 0.3 with a supergene

Allele frequencies in the final generation of all of the runs - non-parental nest survival = 0.4

Trait values in the final generation of all the runs: non-parent nest survival = 0.4 with a supergene

Allele frequencies in the final generation of all of the runs - non-parental nest survival = 0.5

Trait values in the final generation of all the runs: non-parent nest survival = 0.5 with a supergene

Summary

parameter	default	tested_settings	unlinked	linked	supergene
polygyny	monogamy	polygyny	No effect	Allows polymorphism sometimes	Allows polymorphism sometimes
relative reproductive allocation (courter:non-courter)	8:4 (2)	2:8 (0.25), 4:8 (0.5), 4:4 (1), 8:2 (4)	Nuanced effect. High ratios, courters are always fixed. Low allocations, Courter-Nonparent morph is usually fixed, except at ratio 0.25	Nuanced effect. High ratios generally result in Courter-Parent morph to be fixed, although at very high ratios some polymorphism with Noncourter-Nonparent is observed. At the lowest ratio, usually Courter-Nonparent is fixed instead of Courter-Parent	Low ratios allow polymorphism in some cases
parental nest survival	0.9	0.5, 0.6, 0.7, 0.8	No major effect	No major effect	Low survival results in coevolution of Courter and Non-parent traits
non-parental nest survival	0.1	0.2, 0.3, 0.4, 0.5	No major effect	High survival allows higher frequency of Courter-Nonparent morph	High survival allows polymorphism

The genetic architecture of traits impacts whether variation can be maintained, and the extent of genetic variation that is maintained. Further follow-up:

Do simple FST comparisons between the morphs?
How does the supergene evolve over time?
Other sensitivity paramters, plus the key parameters of interest

Sensitivity analysis with ARTs Analysis

Sarah P. Flanagan

26 February, 2019

Courter Trait

Parent Trait

Courter and Parent Traits

Unlinked QTLs

Polygyny

Reproductive Allocations

Parental nest survival

Non-parental nest survival

Linked QTLs

Polygyny

Reproductive Allocations

Parental nest survival

Non-parental nest survival

QTLs in a supergene

Polygyny

Reproductive Allocations

Parental nest survival

Non-parental nest survival

Summary